In a nutshell …

[…] we run experiments that simulate the application of recourse in practice using various state-of-the-art counterfactual generators and find that all of them induce substantial domain and model shifts.

• Counterfactual Explanation (CE) explain how inputs into a model need to change for it to produce different outputs.
• Counterfactual Explanations that involve realistic and actionable changes can be used for the purpose of Algorithmic Recourse (AR) to help individuals who face adverse outcomes.

Figure 1: Dynamics in Algorithmic Recourse: (a) we have a simple linear classifier trained for binary classification where samples from the negative class (\(y=0\)) are marked in blue and samples of the positive class (\(y=1\)) are marked in orange; (b) the implementation of AR for a random subset of individuals leads to a noticable domain shift; (c) as the classifier is retrained we observe a corresponding model shift; (d) as this process is repeated, the decision boundary moves away from the target class.

Consumer Credit Example

Student Admission Example

Algorithmic Recourse

Even though […] interpretability is of great importance and should be pursued, explanations can, in principle, be offered without opening the “black box”. (Wachter, Mittelstadt, and Russell 2017)

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From individual recourse …

• We include the following generators in our simulation experiments below: REVISE (Joshi et al. 2019), CLUE (Antorán et al. 2020), DiCE (Mothilal, Sharma, and Tan 2020) and a greedy approach that relies on probabilistic models (Schut et al. 2021).
• All of them can be described by the following generalized form of Equation @ref(eq:general):

\[ \begin{aligned} \mathbf{s}^\prime &= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \left\{ {\text{yloss}(M(f(\mathbf{s}^\prime)),y^*)}+ \lambda {\text{cost}(f(\mathbf{s}^\prime)) } \right\} \end{aligned} \qquad(3)\]

• Here \(\mathbf{s}^\prime=\left\{s_k^\prime\right\}_K\) is a \(K\)-dimensional array of counterfactual states and \(f: \mathcal{S} \mapsto \mathcal{X}\) maps from the counterfactual state space to the feature space.

… towards collective recourse

• All of the different approaches introduced above tackle the problem of Algorithmic Recourse from the perspective of one single individual.
• We propose to extend Equation Equation 3 as follows:

\[ \begin{aligned} \mathbf{s}^\prime &= \arg \min_{\mathbf{s}^\prime \in \mathcal{S}} \{ {\text{yloss}(M(f(\mathbf{s}^\prime)),y^*)} \\ &+ \lambda_1 {\text{cost}(f(\mathbf{s}^\prime))} + \lambda_2 {\text{extcost}(f(\mathbf{s}^\prime))} \} \end{aligned} \qquad(4)\]

• Here \(\text{cost}(f(\mathbf{s}^\prime))\) denotes the proxy for private costs faced by the individual as before and \(\lambda_1\) governs to what extent that private cost ought to be penalized.
• The newly introduced term \(\text{extcost}(f(\mathbf{s}^\prime))\) is meant to capture and address external costs incurred by the collective of individuals in response to changes in \(\mathbf{s}^\prime\).
• The underlying concept of private and external costs is borrowed from Economics and well-established in that field: when the decisions or actions by some individual market participant generate external costs, then the market is said to suffer from negative externalities and is considered inefficient (Pindyck and Rubinfeld 2014).

Research Questions

Simulations

Evaluation Metrics

\(M\)—Classifiers and Generative Models

tab <- data.frame(
  "Model" = c("MLP","MLP","VAE","VAE"),
  "Data" = c("Synthetic", "Real-World", "Synthetic", "Real-World"),
  "Hidden" = c(32,64,32,32),
  "Latent" = c("-","-",2,8),
  "Layers" = c(1,2,1,1),
  "Batch" = c("-",500,"-","-"),
  "Dropout" = c("-",0.1,"-","-"),
  "Epochs" = c(100,100,100,250)
)
library(kableExtra)
kbl(
  tab, booktabs = TRUE,
  caption = 'Neural network architectures and training parameters.',
  col.names = c("Model","Data","Hidden Dim.","Latent Dim.","Hidden Layers", "Batch", "Dropout", "Epochs")
) |> 
  collapse_rows(1:2, row_group_label_position = 'stack') |>
  kable_styling(latex_options = c("scale_down"))

\(\mathcal{D}\)—Data

Synthetic Data

We use four synthetic binary classification datasets consisting of 1000 samples each: Overlapping, Linearly Separable, Circles and Moons Figure 3.

Figure 3: Synthetic classification datasets used in our experiments. Samples from the negative class (\(y=0\)) are marked in blue while samples of the positive class (\(y=1\)) are marked in orange.

Real-World Data

We use three different real-world datasets from the Finance and Economics domain, all of which are tabular and can be used for binary classification.

1. The Give Me Some Credit dataset: predict whether a borrower is likely to experience financial difficulties in the next two years (Kaggle 2011).
2. The UCI defaultCredit dataset (Yeh and Lien 2009): a benchmark dataset that can be used to train binary classifiers to predict the whether credit card clients default on their payment.
3. The California Housing dataset Pace and Barry (1997): continuous outcome variable binarized as \(\tilde{y}=\mathbb{I}_{y>\text{median}(Y)}\) indicating if the median house price of a given district is above the median of all districts.

\(G\)—Generators

• All generators introduced earlier are included in the experiments: Wachter (Wachter, Mittelstadt, and Russell 2017), REVISE (Joshi et al. 2019), CLUE (Antorán et al. 2020), DiCE (Mothilal, Sharma, and Tan 2020) and Greedy (Schut et al. 2021).
• In addition, we introduce two new generators in Section @ref(mitigate) that directly address the issue of endogenous domain and model shifts. We also test to what extent it may be beneficial to combine ideas underlying the various generators.

More Resources 📚

Image Sources

• Quarto logo. Source: Quarto
• Julia to Quarto animation. Source: author (heavily borrowing from Javis.jl tutorial)